tan-example (used to crash)

Average Accuracy: 79.0% → 99.7%

Time: 37.5s

Precision: binary64

Cost: 45888

\[\left(\left(\left(x = 0 \lor 0.5884142 \leq x \land x \leq 505.5909\right) \land \left(-1.796658 \cdot 10^{+308} \leq y \land y \leq -9.425585 \cdot 10^{-310} \lor 1.284938 \cdot 10^{-309} \leq y \land y \leq 1.751224 \cdot 10^{+308}\right)\right) \land \left(-1.776707 \cdot 10^{+308} \leq z \land z \leq -8.599796 \cdot 10^{-310} \lor 3.293145 \cdot 10^{-311} \leq z \land z \leq 1.725154 \cdot 10^{+308}\right)\right) \land \left(-1.796658 \cdot 10^{+308} \leq a \land a \leq -9.425585 \cdot 10^{-310} \lor 1.284938 \cdot 10^{-309} \leq a \land a \leq 1.751224 \cdot 10^{+308}\right)\]

\[ \begin{array}{c}[y, z] = \mathsf{sort}([y, z])\\ \end{array} \]

Math

\[x + \left(\tan \left(y + z\right) - \tan a\right) \]

↓

\[x + \left(\frac{\tan y + \tan z}{1 - \frac{\frac{\sin y \cdot \sin z}{\cos y}}{\cos z}} - \tan a\right) \]

FPCore

(FPCore (x y z a) :precision binary64 (+ x (- (tan (+ y z)) (tan a))))

↓

(FPCore (x y z a)
 :precision binary64
 (+
  x
  (-
   (/ (+ (tan y) (tan z)) (- 1.0 (/ (/ (* (sin y) (sin z)) (cos y)) (cos z))))
   (tan a))))

C

double code(double x, double y, double z, double a) {
	return x + (tan((y + z)) - tan(a));
}

↓

double code(double x, double y, double z, double a) {
	return x + (((tan(y) + tan(z)) / (1.0 - (((sin(y) * sin(z)) / cos(y)) / cos(z)))) - tan(a));
}

Fortran

real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    code = x + (tan((y + z)) - tan(a))
end function

↓

real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    code = x + (((tan(y) + tan(z)) / (1.0d0 - (((sin(y) * sin(z)) / cos(y)) / cos(z)))) - tan(a))
end function

Java

public static double code(double x, double y, double z, double a) {
	return x + (Math.tan((y + z)) - Math.tan(a));
}

↓

public static double code(double x, double y, double z, double a) {
	return x + (((Math.tan(y) + Math.tan(z)) / (1.0 - (((Math.sin(y) * Math.sin(z)) / Math.cos(y)) / Math.cos(z)))) - Math.tan(a));
}

Python

def code(x, y, z, a):
	return x + (math.tan((y + z)) - math.tan(a))

↓

def code(x, y, z, a):
	return x + (((math.tan(y) + math.tan(z)) / (1.0 - (((math.sin(y) * math.sin(z)) / math.cos(y)) / math.cos(z)))) - math.tan(a))

Julia

function code(x, y, z, a)
	return Float64(x + Float64(tan(Float64(y + z)) - tan(a)))
end

↓

function code(x, y, z, a)
	return Float64(x + Float64(Float64(Float64(tan(y) + tan(z)) / Float64(1.0 - Float64(Float64(Float64(sin(y) * sin(z)) / cos(y)) / cos(z)))) - tan(a)))
end

MATLAB

function tmp = code(x, y, z, a)
	tmp = x + (tan((y + z)) - tan(a));
end

↓

function tmp = code(x, y, z, a)
	tmp = x + (((tan(y) + tan(z)) / (1.0 - (((sin(y) * sin(z)) / cos(y)) / cos(z)))) - tan(a));
end

Wolfram

code[x_, y_, z_, a_] := N[(x + N[(N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_, a_] := N[(x + N[(N[(N[(N[Tan[y], $MachinePrecision] + N[Tan[z], $MachinePrecision]), $MachinePrecision] / N[(1.0 - N[(N[(N[(N[Sin[y], $MachinePrecision] * N[Sin[z], $MachinePrecision]), $MachinePrecision] / N[Cos[y], $MachinePrecision]), $MachinePrecision] / N[Cos[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 79.0%

   \[x + \left(\tan \left(y + z\right) - \tan a\right) \]

2. Applied egg-rr 99.7%

   \[\leadsto x + \left(\color{blue}{\left(\tan y + \tan z\right) \cdot \frac{1}{1 - \tan y \cdot \tan z}} - \tan a\right) \]
   Proof

   [Start] 79.0	\[ x + \left(\tan \left(y + z\right) - \tan a\right) \]
   tan-sum [=>] 99.7	\[ x + \left(\color{blue}{\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z}} - \tan a\right) \]
   div-inv [=>] 99.7	\[ x + \left(\color{blue}{\left(\tan y + \tan z\right) \cdot \frac{1}{1 - \tan y \cdot \tan z}} - \tan a\right) \]

3. Simplified 99.7%

   \[\leadsto x + \left(\color{blue}{\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z}} - \tan a\right) \]
   Proof

   [Start] 99.7	\[ x + \left(\left(\tan y + \tan z\right) \cdot \frac{1}{1 - \tan y \cdot \tan z} - \tan a\right) \]
   associate-*r/ [=>] 99.7	\[ x + \left(\color{blue}{\frac{\left(\tan y + \tan z\right) \cdot 1}{1 - \tan y \cdot \tan z}} - \tan a\right) \]
   *-rgt-identity [=>] 99.7	\[ x + \left(\frac{\color{blue}{\tan y + \tan z}}{1 - \tan y \cdot \tan z} - \tan a\right) \]

4. Applied egg-rr 99.7%

   \[\leadsto x + \left(\frac{\tan y + \tan z}{1 - \color{blue}{\frac{\frac{\sin y \cdot \sin z}{\cos y}}{\cos z}}} - \tan a\right) \]
   Proof

   [Start] 99.7	\[ x + \left(\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z} - \tan a\right) \]
   tan-quot [=>] 99.7	\[ x + \left(\frac{\tan y + \tan z}{1 - \color{blue}{\frac{\sin y}{\cos y}} \cdot \tan z} - \tan a\right) \]
   tan-quot [=>] 99.7	\[ x + \left(\frac{\tan y + \tan z}{1 - \frac{\sin y}{\cos y} \cdot \color{blue}{\frac{\sin z}{\cos z}}} - \tan a\right) \]
   frac-times [=>] 99.7	\[ x + \left(\frac{\tan y + \tan z}{1 - \color{blue}{\frac{\sin y \cdot \sin z}{\cos y \cdot \cos z}}} - \tan a\right) \]
   associate-/r* [=>] 99.7	\[ x + \left(\frac{\tan y + \tan z}{1 - \color{blue}{\frac{\frac{\sin y \cdot \sin z}{\cos y}}{\cos z}}} - \tan a\right) \]

5. Final simplification 99.7%

   \[\leadsto x + \left(\frac{\tan y + \tan z}{1 - \frac{\frac{\sin y \cdot \sin z}{\cos y}}{\cos z}} - \tan a\right) \]

Alternatives

Alternative 1
Accuracy	89.2%
Cost	39881

\[\begin{array}{l} t_0 := \tan y + \tan z\\ \mathbf{if}\;\tan a \leq -5 \cdot 10^{-6} \lor \neg \left(\tan a \leq 2 \cdot 10^{-8}\right):\\ \;\;\;\;x + \left(\frac{t_0}{1 - \frac{\tan z}{y \cdot -0.3333333333333333 + \frac{1}{y}}} - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t_0}{1 - \tan y \cdot \tan z}\\ \end{array} \]

Alternative 2
Accuracy	99.7%
Cost	32832

\[x + \left(\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z} - \tan a\right) \]

Alternative 3
Accuracy	88.7%
Cost	26569

\[\begin{array}{l} \mathbf{if}\;a \leq -1.65 \cdot 10^{-6} \lor \neg \left(a \leq 1.28 \cdot 10^{-8}\right):\\ \;\;\;\;x + \left(\tan \left(y + z\right) - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\tan y + \tan z}{1 - \tan y \cdot \tan z}\\ \end{array} \]

Alternative 4
Accuracy	69.3%
Cost	13385

\[\begin{array}{l} \mathbf{if}\;a \leq -0.001 \lor \neg \left(a \leq 0.0008\right):\\ \;\;\;\;x + \left(\tan y - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;\tan \left(y + z\right) + \left(x - a\right)\\ \end{array} \]

Alternative 5
Accuracy	79.0%
Cost	13248

\[x + \left(\tan \left(y + z\right) - \tan a\right) \]

Alternative 6
Accuracy	58.8%
Cost	7241

\[\begin{array}{l} \mathbf{if}\;y + z \leq -0.1 \lor \neg \left(y + z \leq 5 \cdot 10^{-16}\right):\\ \;\;\;\;x + \tan \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;y + \left(x - \tan a\right)\\ \end{array} \]

Alternative 7
Accuracy	49.9%
Cost	6720

\[x + \tan \left(y + z\right) \]

Alternative 8
Accuracy	31.3%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023135 
(FPCore (x y z a)
  :name "tan-example (used to crash)"
  :precision binary64
  :pre (and (and (and (or (== x 0.0) (and (<= 0.5884142 x) (<= x 505.5909))) (or (and (<= -1.796658e+308 y) (<= y -9.425585e-310)) (and (<= 1.284938e-309 y) (<= y 1.751224e+308)))) (or (and (<= -1.776707e+308 z) (<= z -8.599796e-310)) (and (<= 3.293145e-311 z) (<= z 1.725154e+308)))) (or (and (<= -1.796658e+308 a) (<= a -9.425585e-310)) (and (<= 1.284938e-309 a) (<= a 1.751224e+308))))
  (+ x (- (tan (+ y z)) (tan a))))